The Hibernian Supporters Association, which is understood to have the backing of 14 other groups which represent the club's fans, requested face-to-face talks following the club's relegation from the top flight.
In a statement on Sunday evening, Petrie dismissed any suggestion that he would quit but he has agreed to meet with the protagonists calling for a regime change at Easter Road.
Mike Riley, the chairman of the HSA, will be present at the meeting in Edinburgh, as will former Hibs player Paul Kane and the son of former Hibernian vice-chairman Kenny McLean, Kenny McLean Jr. It is understood they will urge Petrie to relinquish his role as chairman after 10 years at the helm.
It is unclear, however, whether the incoming chief executive Leeann Dempster will attend the meeting, since she does not officially begin her role until June 1.
The appointment of Dempster at the Leith club following her success at Motherwell had been heralded as a sign that Hibs would be revamped both on and off the pitch. However, many fans have not been appeased and are concerned that the changes necessary will not be implemented while Petrie holds the reins.
The HSA are "not confident" that Petrie will be receptive to the idea of stepping aside but still plan to press ahead with a bid to force the chairman out of office. The group will outline their proposals tomorrow and are understood to have gained the backing of business figures within the city and several former players. The details of their plans remain unclear, although a call for a season-ticket boycott is a possibility.
"The fans want Petrie out, the fans want a total change, they have no confidence in him whatsoever," said Riley. "We are down and how long are we going to stay down? Are we going to come back up? Where is the club going? That's why we are determined.
"Everything you can think of is on the agenda, it doesn't require an intelligent person to work out what we can do. We won't relent on this. We know what the fans want and we will be pushing for it."
The plight of Hibs and the club's descent into the SPFL Championship has also proved arresting for former Hibs goalkeeper Alan Rough. He had been far from impressed by the form shown by the Easter Road side this season but never envisaged that the club would actually be relegated.
"It wasn't a surprise they were in the bottom half of the table," he said. "But I didn't think things would deteriorate as badly as they did."